CAIRO — Egypt’s military ruler vowed on Sunday to deal forcefully with the perpetrators of violence as supporters of the country’s ousted Islamist president took to the streets for a third consecutive day to protest the killings of hundreds of anti-government demonstrators over the past four days.

Defense Minister Gen. Abdel Fatah al-Sissi, who led the July 3 coup that toppled President Mohamed Morsi, also said that supporters of the ousted regime would be welcome to participate in politics in the future, but it was unclear whether the offer extended to members of Morsi’s Muslim Brotherhood organization.

The interim government installed by Sissi has hinted that it is considering instituting a ban on the Brotherhood, amid repeated accusations in the media and from government officials that supporters of the Brotherhood are “terrorists” and are responsible for the violence of the past days in which more than 800 people and 70 members of the security forces have been killed.

“We will not be silent in the face of the destruction of the country and the people, of the burning of the homeland and terrorizing innocent people,” Sissi said, adding that Morsi supporters are welcome “to participate in rebuilding of the democratic path and to engage in the political process, according to the map of the future rather than confrontation and destruction of the Egyptian state.”

The interim government also announced that it was banning the formation of Popular Committees, the vigilante groups blamed by the protesters for much of the violence that erupted on Friday. “To enforce the law . . . the Ministry of Interior has decided to prevent the establishment of the People’s Committees which are exploited by others to conduct acts against the law,” said a statement on the ministry’s Facebook page.

Yet even as the authorities seemed to be trying to tamp down the violence, the Anti-Coup Alliance representing Morsi’s supporters said 38 detainees rounded up during the recent demonstrations were killed by police while they were being transferred to prison.

The Ministry of Interior reported that 612 prisoners had attempted to escape, and the Masry el-Youm newspaper quoted police as saying 38 were killed, saying they had been suffocated. The Alliance said they were killed in their vehicle with gunshots and tear gas fired through the windows.

Thousands of Morsi supporters took to the streets again on Sunday to condemn the harsh tactics used by the security forces in their efforts to quell those challenging the army takeover.

The Egyptian military went to extraordinary lengths to protect the site of the main protest called for Sunday — the Supreme Constitutional Court in Cairo. Security forces ringed it with armored personnel carriers and closed nearby streets with concertina wire and iron barricades. Camouflage-clad soldiers, riot police in black uniforms and body armor, and traffic police milled around the building, weapons at the ready.

About a mile away, a group of about 60 supporters of Morsi said they had had to thread through neighborhoods with closed roads and menacing security forces.

“I saw thugs with molotov cocktails,” said one Muslim Brotherhood supporter, a 60-year-old woman in a long black robe and pink veil. She said that she saw one protester get beaten when he attempted to pass through a roadblock set up by security forces.

On Saturday, Egyptian security forces overran a Cairo mosque in which hundreds of Morsi supporters had barricaded themselves for nearly 24 hours after a day of gun battles in the heart of the capital.

The protesters were detained after security forces had escorted them from the al-Fateh mosque, and Egyptian state television declared that “the crisis is over.”

But Saturday brought demonstrations and clashes in several other cities across the country. The Muslim Brotherhood and the Anti-Coup Alliance called for more protests — every day for the coming week — in the same central square where hundreds of pro-Morsi protesters were killed Friday. The group vowed that the protesters would perform their evening prayer there.

Under the government’s increasingly violent crackdown, the voices of Morsi’s supporters have gradually slipped offline and off their defiant protest stages. Much of the leadership of the Brotherhood, which led two sprawling protest camps until they were cleared in a deadly assault Wednesday, is now in jail, missing or in hiding. Now, a host of young people, wives and other relatives of the missing Islamist leaders who once ran this country have become the spokesmen for a protest movement that is now swiftly losing power but is no less defiant.

On Saturday, the standoff at al-Fateh mosque erupted suddenly into a prolonged gunfight, the chaos and panic spilling into side streets and the wider neighborhood as security forces opened fire and shots were returned from the mosque’s minaret and windows. The protesters, including medical personnel and the wounded, had on Friday taken refuge in the mosque from gunfire outside in Ramses Square on a day of widespread violence that left at least 230 people dead nationwide.

Abigail Hauslohner has been The Post’s Cairo bureau chief since 2012. She served previously as a Middle East correspondent for Time magazine and has been covering the Middle East since 2007.

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